Topological groups and C-embeddings

The notion of a Moscow space is applied to the study of some problems of topological algebra, following an approach introduced by AX Arhangel'skii [Comment. Math. Univ. Carolin. 41 (2000) 585-595]. In particular, many new, and, it seems, unexpected, solutions to the equation vX x vY = v(X x Y) are identified. We also find new large classes of topological groups G, for which the operations in G can be extended to the Dieudonne completion of the space G in such a way that G becomes a topological subgroup of the topological group muG. On the other hand, it was shown by AX Arhangel'skii [Comment. Math. Univ. Carolin. 41 (2000) 585-595] that there exists an Abelian topological group G for which such an extension is impossible (this provided an answer to a question of V.G. Pestov and M.G. Tkacenko, dating back to 1985). Some new open questions are formulated. (C) 2001 Elsevier Science B.V. All rights reserved.